Question : Three containers have their volumes in the ratio 3 : 4 : 5. They are full of mixtures of milk and water. The mixtures contain milk and water in the ratios (4 : 1), (3 : 1), and (5 : 2), respectively. The contents of all these three containers are poured into a fourth container. The ratio of milk and water in the fourth container is:
Option 1: 4 : 1
Option 2: 151 : 48
Option 3: 157 : 53
Option 4: 5 : 2
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Correct Answer: 157 : 53
Solution :
Let the volumes of the three containers be $3x$, $4x$, and $5x$.
In the container with volume $3x$,
Milk $=\frac{4}{4+1}×3x=\frac{12x}{5}$
Water $=\frac{1}{4+1}×3x=\frac{3x}{5}$
In the container with volume $4x$,
Milk $=\frac{3}{3+1}×4x=\frac{12x}{4}$
Water $= \frac{1}{3+1}×4x=\frac{4x}{4}$
In the container with volume $5x$,
Milk $= \frac{5}{5+2}×5x=\frac{25x}{7}$
Water $=\frac{2}{5+2}×5x=\frac{10x}{7}$
Total milk $=\frac{12x}{5}+\frac{12x}{4}+\frac{25x}{7}=\frac{336x+420x+500x}{140}=\frac{1256x}{140}$
Total water $=\frac{3x}{5}+\frac{4x}{4}+\frac{10x}{7}=\frac{84x+140x+200x}{140}=\frac{424x}{140}$
The ratio of milk to water in the 4
th
container $=\frac{1256}{424}=157:53$
Hence, the correct answer is 157 : 53.
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